Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

The spectacular progress made during the last few years in reaching high energy densities in fast implosions of annular current sheaths (fast Z pinches) opens new possibilities for a broad spectrum of experiments, from x-ray generation to controlled thermonuclear fusion and astrophysics. Presently Z pinches are the most intense laboratory X ray sources (1.8 MJ in 5 ns from a volume 2 mm in diameter and 2 cm tall). Powers in excess of 200 TW have been obtained. This warrants summarizing the present knowledge of physics that governs the behavior of radiating current-carrying plasma in fast Z pinches. This survey covers essentially all aspects of the physics of fast Z pinches: initiation, instabilities of the early stage, magnetic Rayleigh-Taylor instability in the implosion phase, formation of a transient quasi-equilibrium near the stagnation point, and rebound. Considerable attention is paid to the analysis of hydrodynamic instabilities governing the implosion symmetry. Possible ways of mitigating these instabilities are discussed. Non-magnetohydrodynamic effects (anomalous resistivity, generation of particle beams, etc.) are summarized. Various applications of fast Z pinches are briefly described. Scaling laws governing development of more powerful Z pinches are presented. The survey contains 36 figures and more than 300 references.

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The physics of fast Z pinches

The direct-drive, laser-based approach to inertial confinement fusion (ICF) is reviewed from its inception following the demonstration of the first laser to its implementation on the present generation of high-power lasers. The review focuses on the evolution of scientific understanding gained from target-physics experiments in many areas, identifying problems that were demonstrated and the solutions implemented. The review starts with the basic understanding of laser–plasma interactions that was obtained before the declassification of laser-induced compression in the early 1970s and continues with the compression experiments using infrared lasers in the late 1970s that produced thermonuclear neutrons. The problem of suprathermal electrons and the target preheat that they caused, associated with the infrared laser wavelength, led to lasers being built after 1980 to operate at shorter wavelengths, especially 0.35 μm—the third harmonic of the Nd:glass laser—and 0.248 μm (the KrF gas laser). The main physics areas relevant to direct drive are reviewed. The primary absorption mechanism at short wavelengths is classical inverse bremsstrahlung. Nonuniformities imprinted on the target by laser irradiation have been addressed by the development of a number of beam-smoothing techniques and imprint-mitigation strategies. The effects of hydrodynamic instabilities are mitigated by a combination of imprint reduction and target designs that minimize the instability growth rates. Several coronal plasma physics processes are reviewed. The two-plasmon–decay instability, stimulated Brillouin scattering (together with cross-beam energy transfer), and (possibly) stimulated Raman scattering are identified as potential concerns, placing constraints on the laser intensities used in target designs, while other processes (self-focusing and filamentation, the parametric decay instability, and magnetic fields), once considered important, are now of lesser concern for mainline direct-drive target concepts. Filamentation is largely suppressed by beam smoothing. Thermal transport modeling, important to the interpretation of experiments and to target design, has been found to be nonlocal in nature. Advances in shock timing and equation-of-state measurements relevant to direct-drive ICF are reported. Room-temperature implosions have provided an increased understanding of the importance of stability and uniformity. The evolution of cryogenic implosion capabilities, leading to an extensive series carried out on the 60-beam OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)], is reviewed together with major advances in cryogenic target formation. A polar-drive concept has been developed that will enable direct-drive–ignition experiments to be performed on the National Ignition Facility [Haynam et al., Appl. Opt. 46(16), 3276 (2007)]. The advantages offered by the alternative approaches of fast ignition and shock ignition and the issues associated with these concepts are described. The lessons learned from target-physics and implosion experiments are taken into account in ignition and high-gain target designs for laser wavelengths of 1/3 μm and 1/4 μm. Substantial advances in direct-drive inertial fusion reactor concepts are reviewed. Overall, the progress in scientific understanding over the past five decades has been enormous, to the point that inertial fusion energy using direct drive shows significant promise as a future environmentally attractive energy source.

Direct-drive inertial confinement fusion: A review

The interactions between acoustic waves and a premixed combustion process can play an important role in the characteristicunsteadinessofcombustiondevices.Inparticular,theyareoftenresponsiblefortheoccurrenceofselfexcited, combustion-driven oscillations that are detrimental to combustor life and performance. A tutorial review is provided of current understanding of these interactions. First, the mutual interaction mechanisms between the combustion process and acoustic, vorticity, and entropy waves are described. Then, the acoustic‐ e ame interaction literatureisreviewed,primarily focusingon modeling issues.Thisliteratureisessentially organized into fourparts, depending on its treatment of 1) linear or 2) nonlinear analyses of 1) e amelets or 2) distributed reaction zones. A sizeable theoretical literature has accumulated to model the unsteady response of the laminar e ame structure, for example, the burning rate response to pressure perturbations. However, essentially no serious experimental effort has been performed to critically assess these predictions. As such, it is dife cult to determine the state of understanding in this area. On the other hand, good agreement has been achieved between well-coordinated experiments and theory describing the interactions between inherent e ame instabilities and acoustically induced e ow oscillations. Similarly, both the linear and nonlinear kinematic response of simple laminar e ames to acoustic velocity disturbances appear to be well understood, as evidenced by the agreement between surprisingly simple theory and experiment. Other than kinematic nonlinearities, additional potential mechanisms that introduce heat release‐ acoustic nonlinearities, such as e ame holding, or extinction, have been analyzed theoretically, but lack experimentalverie cation.Unsteadyreactormodelshavebeenusedextensivelytomodelcombustionprocessesinthe distributed reaction zone regimes. None of thesepredictionsappears to have been subjected to direct experimental scrutiny. Itisunlikelythatthismodeling approach willbeusefulforquantitativecombustion responsecalculations, due to their largely heuristic nature and the dife culty in rationally modeling the key interactions between reaction rate and the global characteristics of the combustion region, such as its volume. Several areas in need of work are particularly highlighted. These include e nite amplitude effects, modeling approaches for interactions outside of the e amelet regime, turbulent e ame wrinkling effects, and unsteady vortex‐ e ame interactions.

Modeling Premixed Combustion-Acoustic Wave Interactions: A Review

Hydrodynamic and hydromagnetic stability

Dynamics and stability of premixed flames

A nonlinear equation for a curved stationary flame subject to the Darrieus–Landau instability is obtained for an arbitrary ratio of the fuel density and the density of the burnt matter under the assumptions of a thin flame front and weak nonlinearity. On the basis of the nonlinear equation the velocity of a two-dimensional curved stationary flame is calculated. The obtained velocity is in a good agreement with the results of two-dimensional simulations of flame dynamics in tubes.

Nonlinear equation for a curved stationary flame and the flame velocity

Analytical scalings for the problem of flame interaction with acoustic waves of controlled intensity are obtained on the basis of the linear equation for a perturbed flame front. Both stabilization of the hydrodynamic flame instability by sound waves of small amplitudes and excitation of the parametric instability at the flame front by sound waves of sufficiently large amplitudes are considered. The stability limits obtained analytically agree well with the previous numerical calculations. Besides, the analytical results for the minimum amplitude of sound waves needed to induce the parametric instability and for the typical wavelength of the instability are in excellent agreement with the experimental results on propane flames.

Analytical scalings for flame interaction with sound waves

A self‐consistent approach to the problem of the growth rate of the Rayleigh–Taylor instability in laser accelerated targets is developed. The analytical solution of the problem is obtained by solving the complete system of the hydrodynamical equations which include both thermal conductivity and energy release due to absorption of the laser light. The developed theory provides a rigorous justification for the supplementary boundary condition in the limiting case of the discontinuity model. An analysis of the suppression of the Rayleigh–Taylor instability by the ablation flow is done and it is found that there is a good agreement between the obtained solution and the approximate formula σ = 0.9√gk − 3u1k, where g is the acceleration, u1 is the ablation velocity. This paper discusses different regimes of the ablative stabilization and compares them with previous analytical and numerical works.

Self‐consistent model of the Rayleigh–Taylor instability in ablatively accelerated laser plasma

Flame dynamics in wide tubes with ideally adiabatical and slip walls is studied by means of direct numerical simulations of the complete set of hydrodynamical equations including thermal conduction, fuel diffusion, viscosity, and chemical kinetics. Stability limits of curved stationary flames in wide tubes and the hydrodynamic instability of these flames (the secondary Darrieus-Landau instability) are investigated. The stability limits found in the present numerical simulations are in a very good agreement with the previous theoretical predictions. It is obtained that close to the stability limits the secondary Darrieus-Landau instability results in an extra cusp at the flame front. It is shown that the curved flames subject to the secondary Darrieus-Landau instability propagate with velocity considerably larger than the velocity of the stationary flames.

V. V. Bychkov

Papers

Dynamics and stability of premixed flames

Nonlinear equation for a curved stationary flame and the flame velocity

Analytical scalings for flame interaction with sound waves

Self‐consistent model of the Rayleigh–Taylor instability in ablatively accelerated laser plasma

Numerical studies of flames in wide tubes: stability limits of curved stationary flames